Conjugate-pairing rule and thermal-transport coefficients

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Abstract
It has recently been shown by Evans, Cohen, and Morriss [Phys. Rev. A 42, 5990 (1990)] that bulk thermal-transport coefficients can be calculated from the maximal Lyapunov exponents by using the conjugate-pairing rule. In the present paper we use computer simulation to explore the validity of the rule under conditions which are more general than those used in the derivation by Evans, Cohen, and Morriss. We show that the existence of a IsteadyP state for dissipative dynamics and the satisfaction of the condition known as the adiabatic incompressibility of phase space (i.e., area preserving in the absence of a thermostat) are insufficient for the rule to hold. We also show that the linear field-induced shift of the Lyapunov exponents with respect to the exponent index, is among the nonequilibrium molecular-dynamics algorithms, apparently peculiar to the SLLOD algorithm (so named because of its close relationship to the Dolls tensor algorithm) for shear flow.

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